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UID:33@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20240131T140000
DTEND;TZID=Asia/Kolkata:20240131T150000
DTSTAMP:20240126T064012Z
URL:https://cds.iisc.ac.in/events/ph-d-thesis-defense-online-mode-cds-31-j
 anuary-2024-sparsification-of-reaction-diffusion-dynamical-systems-on-comp
 lex-networks/
SUMMARY:Ph.D: Thesis Defense: Online Mode: CDS: 31\, January 2024 "Sparsifi
 cation of Reaction-Diffusion Dynamical Systems on > Complex Networks"
DESCRIPTION:DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES\n\nPh.D. Thesis D
 efense\n\n\n\nSpeaker : Mr.Abhishek Ajayakumar\n\nS.R. Number : 06-18-01-1
 0-12-18-1-16176\n\nTitle : "Sparsification of Reaction-Diffusion Dynamical
  Systems on Complex Networks"\n\nResearch Supervisor : Prof. Soumyendu Rah
 a\n\nDate &amp\; Time : January 31\, 2024 (Wednesday)\, 02:00 PM\nVenue : 
 The Thesis Défense will be held on MICROSOFT TEAMS\n\nPlease click on the
  following link to join the Thesis Defense:\n\nMS Teams link\n\n\n\nABSTRA
 CT\n\nGraph sparsification is an area of interest in computer science and 
 applied mathematics. Sparsification of a graph\, in general\, aims to redu
 ce the number of edges in the network while preserving specific properties
  of the graph\, like cuts and subgraph counts. Modern deep learning framew
 orks\, which utilize recurrent neural network decoders and convolutional n
 eural networks\, are characterized by a significant number of parameters. 
 Pruning redundant edges in such networks and rescaling the weights can be 
 useful. Computing the sparsest cuts of a graph is known to be NP-hard\, an
 d sparsification routines exist for generating linear-sized sparsifiers in
  almost quadratic running time.The complexity of this task varies\, closel
 y linked to the desired level of sparsity to achieve. The thesis introduce
 s the concept of sparsification to the realm of reaction-diffusion complex
  systems. The aim is to address the challenge of reducing the number of ed
 ges in the network while preserving the underlying flow dynamics. Sparsifi
 cation of such complex networks is approached as an inverse problem guided
  by data representing flows in the network\, where a relaxed approach is a
 dopted considering only a subset of trajectories. The network sparsificati
 on problem is mapped to a data assimilation problem on a reduced order mod
 el (ROM) space with constraints targeted at preserving the eigenmodes of t
 he Laplacian matrix under perturbations. The Laplacian matrix is the diffe
 rence between the diagonal matrix of degrees and the graph’s adjacency m
 atrix. Approximations are propose to the eigenvalues and eigenvectors of t
 he Laplacian matrix subject to perturbations for computational feasibility
 \, and a custom function is included based on these approximations as a co
 nstraint on the data assimilation framework. Extensive empirical testing c
 overed a range of graphs\, while its application to multiple instances led
  to the creation of sparse graphs. In the latter phase of the thesis\, a f
 ramework is presented to enhance proper orthogonal decomposition (POD)-bas
 ed model reduction techniques in reaction-diffusion complex systems. This 
 framework incorporates techniques from stochasticfiltering theory and patt
 ern recognition (PR). Obtaining optimal state estimates from a noisy model
  and noisy measurements forms the core of the filtering problem. By integr
 ating the particle filtering technique\, the reaction-diffusion state vect
 ors are generated at various time steps\, utilizing the ROM states as meas
 urements. To ensure the framework’s effectiveness\, intermittent updates
  to the system variables are made during the particle filtering step\,empl
 oying the carefully crafted sparse graph. The framework is utilized for ex
 perimentation\, and results are presented on random graphs\, considering t
 he diffusion equation on the graph and the chemical Brusselator model as t
 he reaction-diffusion system embedded in the graph. Limitations of the met
 hod are discussed\, and the proposed framework is evaluated by comparing i
 ts performance against the Neural Ordinary Differential Equation or neural
  ODE-based approach\, which serves as a compelling reference due to its de
 monstrated robustness in specific applications.\n\n\n\nALL ARE WELCOME
CATEGORIES:Events,Thesis Defense
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